Vatrano got his 12th goal when he beat Petr Mrazek from the left side of the net. Isac Lundestrom set up the game-winner with a cross-ice pass.
''It was a great play by Lundy all around, to hold on to that puck and find a lane for me,'' Vatrano said.
The Ducks improved to 4-0-1 in their last five games. It was Anaheim's first win against Chicago since Dec. 5, 2018, stopping an eight-game slide.
''We've been going good as of late and before the (All-Star) break we were playing some good hockey,'' Vatrano said. ''We wanted to start after the break with some positivity.''
Brett Leason and Jayson Megna each had a goal and an assist for Anaheim (17-29-6). John Klingberg had two assists, and Anthony Stolarz made 27 saves.
''We just kept our heads down and kept swinging,'' Anaheim coach Dallas Eakins said. ''Lundstrom's out there and he shows some patience. Franky Vatrano really woke up there in the third period and continued on to the overtime.''
Chicago's Jason Dickinson had a goal for the third straight game. Seth Jones also scored and Mrazek blocked 23 shots.
With the game tied at 2, the Blackhawks controlled much of the action in the third period. But Stolarz stopped Dickinson's point-blank shot with 7:40 left. Chicago defenseman Jake McCabe missed on a prime chance with just over six minutes remaining.
''Yeah, that one hurts,'' Dickinson said. ''Feel like we should have won, but we let that one get away from us.''
It was the first game for the Blackhawks since Hall of Fame forward Bobby Hull died last week at age 84. The organization paid tribute to Hull with a pregame moment of silence and a video of his career highlights.
Troy Terry, Anaheim's All-Star forward, was sidelined by an upper-body injury. He is day to day after he got hurt during a 3-2 shootout loss at Dallas on Monday.
Blackhawks captain Jonathan Toews missed the game with a non-COVID-19 illness.
Dickinson opened the scoring at 1:36 of the second period. He beat Stolarz from the slot after Patrick Kane made a centering pass from the backboards.
Leason tied it at 8:25, knocking in a rebound of his own shot with a one-handed swat.
Jones put Chicago (15-29-5) back in front at 13:09. The All-Star defenseman jumped up to join a rush, took Dickinson's cross-ice feed and connected from the slot.
Megna tied it at 2 at 15:42 with his first goal of the season and No. 11 for his career. He scored from the right circle after Jones lost the puck behind his own net.
Kane said Monday that a few NHL teams had reached out to his agent, Pat Brisson, about a potential trade before the March 3 deadline.
Kane and Toews are in the final seasons of eight-year contracts with no-movement clauses. Both are represented by Brisson and would need to consent to a deal that might bring rebuilding Chicago draft picks or prospects.
Blackhawks C Tyler Johnson (left ankle) returned after missing three games. ... Chicago D Jarred Tinordi, out since Dec. 18 with a broken jaw, has been activated off IR. He could play this weekend. ... F Derek Grant took Terry's place in Anaheim's lineup. ... Chicago D Connor Murphy played his 600th game.
Ducks: Host Pittsburgh on Friday.
Blackhawks: Host Arizona on Friday.
AP NHL: https://apnews.com/hub/nhl and https://twitter.com/AP-Sports
Copyright 2023 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.